Upon cooling, water freezes to ice. This familiar phase transition occurs widely in nature, yet unlike the freezing of simple liquids1, 2, 3, it has never been successfully simulated on a computer. The difficulty lies with the fact that hydrogen bonding between individual water molecules yields a disordered three-dimensional hydrogen-bond network whose rugged and complex global potential energy surface4, 5, 6 permits a large number of possible network configurations. As a result, it is very challenging to reproduce the freezing of 'real' water into a solid with a unique crystalline structure. For systems with a limited number of possible disordered hydrogen-bond network structures, such as confined water, it is relatively easy to locate a pathway from a liquid state to a crystalline structure7, 8, 9. For pure and spatially unconfined water, however, molecular dynamics simulations of freezing are severely hampered by the large number of possible network configurations that exist. Here we present a molecular dynamics trajectory that captures the molecular processes involved in the freezing of pure water. We find that ice nucleation occurs once a sufficient number of relatively long-lived hydrogen bonds develop spontaneously at the same location to form a fairly compact initial nucleus. The initial nucleus then slowly changes shape and size until it reaches a stage that allows rapid expansion, resulting in crystallization of the entire system.